Write the equation of a circle with endpoints of the diameter at (2, -5) and (-4, 3)

Question

zepdrix · Answer

Umm so I guess we need a couple pieces of information.

We need to find the length of the diameter ( which will lead to the radius value).
We can use the distance formula for that.

We also need to find the mid point of the diameter. This will give us the center of our circle.
I'm trying to remember how to find midpoint...
I think we just take the average of the x's and the average of the y's yes?

zepdrix · Answer

This will give us the length of the diameter,
$$\Large\rm d=\sqrt{(-4-2)^2+(3+5)^2}$$Understand how I plugged those values in?

anonymous · Answer

yes

anonymous · Answer

so this is the equation

zepdrix · Answer

no -_-

zepdrix · Answer

The equation of a circle will be of the form:$$\Large\rm (x-h)^2+(y-k)^2=r^2$$Where $\Large\rm (h,k)$ is the center of the circle,
and $\Large\rm r$ is the radius.

zepdrix · Answer

This distance formula will give us the `length of the diameter`.
We can then cut that in half to find our $\large\rm r$ value.

zepdrix · Answer

Then you need to use the mid point formula to find your $\Large\rm (h,k)$ center point.